Data adaptive RKHS Tikhonov regularization for learning kernels in operators Article Swipe

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YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2203.03791

We present DARTR: a Data Adaptive RKHS Tikhonov Regularization method for the linear inverse problem of nonparametric learning of function parameters in operators. A key ingredient is a system intrinsic data-adaptive (SIDA) RKHS, whose norm restricts the learning to take place in the function space of identifiability. DARTR utilizes this norm and selects the regularization parameter by the L-curve method. We illustrate its performance in examples including integral operators, nonlinear operators and nonlocal operators with discrete synthetic data. Numerical results show that DARTR leads to an accurate estimator robust to both numerical error due to discrete data and noise in data, and the estimator converges at a consistent rate as the data mesh refines under different levels of noises, outperforming two baseline regularizers using $l^2$ and $L^2$ norms.

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Reproducing Kernel Hilbert Space

Artificial Intelligence

Mathematical Analysis

Statistics

Law

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Tikhonov regularization Regularization perspectives on support vector machines Regularization (linguistics) Reproducing kernel Hilbert space Mathematics Estimator Applied mathematics Nonparametric statistics Inverse problem Hilbert space Norm (philosophy) Mathematical optimization Computer science Algorithm Artificial intelligence Mathematical analysis Statistics Law Political science

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2203.03791
PDF: https://arxiv.org/pdf/2203.03791
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Cited By: 2
Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.2203.03791

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Title: Data adaptive RKHS Tikhonov regularization for learning kernels in operators

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Language: en

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Publication year: 2022

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Publication date: 2022-03-08

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Authors: Fei Lu, Quanjun Lang, Qingci An

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Concepts: Tikhonov regularization, Regularization perspectives on support vector machines, Regularization (linguistics), Reproducing kernel Hilbert space, Mathematics, Estimator, Applied mathematics, Nonparametric statistics, Inverse problem, Hilbert space, Norm (philosophy), Mathematical optimization, Computer science, Algorithm, Artificial intelligence, Mathematical analysis, Statistics, Law, Political science

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Cited by: 2

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